The  principle of operation is as simple as the circuit itself: When power is applied, the transistor will conduct the current allowed through resistors R1 and R2 into the flyback primary, causing it to induce a current on the secondary, and, at the same time, on the feedback winding. This feedback current will trigger the transistor to stop conducting, and as the magnetic field in the ferrite core collapses, a large HV spike will appear on the secondary windings (basic inductor action). But now there is no feedback current to keep the transistor off, so it will once again conduct, and the cycle will repeat, at a natural frequency that puts the transformer in resonance, resulting in enormous voltage gain. One of the advantages of having a feedback winding is that the circuit becomes dynamic: The frequency of operation is automatically adjusted to resonance, depending on many factors. It is interesting, because you can actually hear the frequency change as you draw an arc (high loads drop the frequency to a high pitched 20Khz whine which than becomes ultrasonic as the arc grows).